Displaying similar documents to “General bounds for identifying codes in some infinite regular graphs.”

The code problem for directed figures

Michał Kolarz (2010)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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We consider directed figures defined as labelled polyominoes with designated start and end points, with two types of catenation operations. We are especially interested in codicity verification for sets of figures, and we show that depending on the catenation type the question whether a given set of directed figures is a code is decidable or not. In the former case we give a constructive proof which leads to a straightforward algorithm.

Lattice-Like Total Perfect Codes

Carlos Araujo, Italo Dejter (2014)

Discussiones Mathematicae Graph Theory

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A contribution is made to the classification of lattice-like total perfect codes in integer lattices Λn via pairs (G, Φ) formed by abelian groups G and homomorphisms Φ: Zn → G. A conjecture is posed that the cited contribution covers all possible cases. A related conjecture on the unfinished work on open problems on lattice-like perfect dominating sets in Λn with induced components that are parallel paths of length > 1 is posed as well.